This is a course in the intermediate and advanced foundations of statistical inference in the context of applied research. Assuming some prior exposure to probability and statistics, this course will cover topics such as the principles of estimation and hypothesis testing, as well as general and generalized linear models, under the Bayesian paradigm. The Bayesian method is developed in depth. The student will be expected to understand the mathematical theory, implement related statistical algorithms in statistical programming language such as R, and interpret models and parameters in the context of applied statistical analysis of real data.